Question

A wire of length L and resistance R is stretched so that its length its doubled. How will

(i) Resistance change (ii) Resistivity change?

• A. Resistance increases 2 times; resistivity remains same
• B. Resistance increases 4 times; resistivity remains same
• C. Resistance decreases 4 times; resistivity increases 2 times
• D. Resistance decreases 2 times; resistivity increases 4 times

Answer 1

The correct option is B

Resistance increases 4 times; resistivity remains same

Volume of wire remains same

$V=L\times A$

So if l increases 2 times so the A should decrease 2 times

New L = 2L; New A = $\frac{A}{2}$

R=$\frac{\rho l}{A}$

New R= $\frac{\rho \times 2\times l\times 2}{A}$ = $\frac{4\times \rho \times l}{A}$ = 4 Old R

As $\rho$ is dependent on temp directly so when temperature increases the resistivity increases.

Here $\rho$ remains unchanged as there is no change in temperature.